Calculation of Entailed Rank Constraints in Partially NonLinear and Cyclic Models
Peter Spirtes
Abstract:
The Trek Separation Theorem (Sullivant et al. 2010) states necessary and sufficient conditions for a linear directed acyclic graphical model to entail for all possible values of its linear coefficients that the rank of various submatrices of the covariance matrix is less than or equal to n, for any given n. In this paper, I extend the Trek Separation Theorem in two ways: I prove that the same necessary and sufficient conditions apply even when the generating model is partially nonlinear and contains some cycles. This justifies application of constraintbased causal search algorithms such as the BuildPureClusters algorithm (Silva et al. 2006) for discovering the causal structure of latent variable models to data generated by a wider class of causal models that may contain nonlinear and cyclic relations among the latent variables.
Keywords:
Pages: 606615
PS Link:
PDF Link: /papers/13/p606spirtes.pdf
BibTex:
@INPROCEEDINGS{Spirtes13,
AUTHOR = "Peter Spirtes
",
TITLE = "Calculation of Entailed Rank Constraints in Partially NonLinear and Cyclic Models",
BOOKTITLE = "Proceedings of the TwentyNinth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI13)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "2013",
PAGES = "606615"
}

